SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1620-1622, January 2020.
Let $a_1,\ldots,a_n$ be a permutation of $[n]$. Two disjoint order-isomorphic subsequences are called twins. We show that every permutation of $[n]$ contains twins of length $\Omega(n^{3/5})$ improving the trivial bound of $\Omega(n^{1/2})$. We also show that a random permutation contains twins of length $\Omega(n^{2/3})$, which is sharp.

中文翻译：

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排列中的同构同卵双胞胎

SIAM离散数学杂志，第34卷，第3期，第1620-1622页，2020年1月。
令$ a_1，\ ldots，a_n $为$ [n] $的排列。两个不相交的阶同构子序列称为孪生子。我们显示$ [n] $的每个排列都包含长度为\\ Omega（n ^ {3/5}）$的双胞胎，从而改善了$ \ Omega（n ^ {1/2}）$的琐碎界限。我们还显示，随机排列包含长度为\\ Omega（n ^ {2/3}）$的双胞胎，这很明显。